By most conventional measures,
Dan Sullivan
looks to be the favorite to win the Republican Senate primary in Alaska.

The former Alaska attorney general and natural resources commissioner has consistently led in polls, has far outraised his two GOP rivals and won support from business groups and grass-roots conservatives. National Democrats have spent more attacking him than any other Republican in the primary season.

But polls in the predominantly rural state can be unreliable, and a little money can buy a lot of TV ad time for a population of under 500,000 registered voters. Charges of carpetbagging are swirling, and there is a tea-party-backed candidate who adds a wild card to the race.

That is why many observers aren't sure who will win next Tuesday's primary and take on one-term incumbent Democratic Sen.
Mark Begich
in November.

A win in the state is crucial to Republican aspirations to regain control of the Senate in November—and to Democratic efforts to ensure that doesn't happen.

While Mr. Sullivan, 49, has high name recognition in the state, so do his rivals: Lieutenant Gov.
Mead Treadwell
and tea party-aligned
Joe Miller,
who won the 2010 GOP Senate primary and then lost the general election to incumbent Republican
Lisa Murkowski,
who ran a write-in campaign.

Some Alaska Republicans fear that if Mr. Miller, 47, loses on Tuesday, he would mount a third-party bid, possibly derailing Republicans' chances of picking up the seat. When asked, Mr. Miller has said he wouldn't commit to any particular path following the primary.

Mr. Sullivan has raised almost three times as much money as his two competitors combined, and has won contributions from, among others, Karl Rove and former President
George W. Bush.
The U.S. Chamber of Commerce and the conservative Club for Growth—who in other states have come down on opposing sides in GOP primaries this year—are supporting him.

But that hasn't stopped the sparring among the candidates, which has largely centered on biography and personality.

Mr. Miller has underscored his small-government appeal by slamming the party establishment and tying illegal immigration, not traditionally a prominent issue in Alaska, to gun rights.

Mr. Treadwell, 58, has adopted some of Mr. Miller's tea-party rhetoric, bucking his own, more moderate record. He appeared to backtrack from comments he had made as Mr. Bush's Arctic Research Commissioner that appeared to recognize human-produced climate change, but said his position on climate science hasn't shifted. "My job was to advocate for appropriate science, and I wanted to make sure all the science was available," he said. "You'll certainly find me talk about each of the theories."

At the same time, he has positioned himself as best equipped to oppose Mr. Begich in November, arguing that his Alaska roots, like Mr. Begich's, run deeper than those of Mr. Sullivan.

Mr. Treadwell's attacks, and those of Democrats, have focused on Mr. Sullivan's out-of-state backing and his childhood roots in Ohio. He once said he had a jar of mayonnaise in his refrigerator that resided in Alaska longer than had Mr. Sullivan.

"The difference [between us] is, I'm running against a public paint company from Ohio," Mr. Treadwell said in an interview, referring to
RPM International,
an Ohio-based company that Mr. Sullivan's family owns.

Those accusations sting in a state that refers to the continental 48 states as simply "outside." Mr. Sullivan, who graduated from Georgetown University Law School, moved to Alaska in 1997 to clerk for a federal judge in Fairbanks. He returned to Washington in 2002, where he held several positions in the Bush administration, then returned to Alaska in 2009 when then-Gov.
Sarah Palin
appointed him state attorney general.

The accusations have clung to Mr. Sullivan despite his popularity, said
Matt Larkin,
a pollster for Dittman Research, which has been hired by Mr. Treadwell. During his years at the State Department, Mr. Sullivan once filed for a Maryland tax credit—a detail the Begich campaign has noted.

Mr. Sullivan campaign countered that "he got married in Fairbanks 20 years ago this month, and became a resident when he got out of the active duty Marines 17 years ago and started his family here in Alaska."

His candidacy is further complicated by another Dan Sullivan on the November ballot—the popular mayor of Anchorage who is running for lieutenant governor.

Ultimately, no matter who prevails in the primary, polls show Mr. Begich with a slight but consistent advantage over his potential Republican rivals.

That helps explain why Democrats think it worthwhile sending money into the race, as they have done, said
Jim Manley,
a former aide to Senate Majority Leader
Harry Reid,
whose Senate Majority PAC already has spent $4 million to attack Mr. Sullivan.

"One of the real reasons [Democrats are] pouring so much money into this race," Mr. Manley said, "is that they think, with a little bit of air cover, they think he's going to win."